Not much around for "mowing only" groups. One bet would be to join Ohio Turf Foundation. Their conference is in early Dec, I think. Not too many local trade assns, but there are some in some areas. Just need to ask around locally.
If you want to make a living out of it, many of the better clients like to have a full service landscape maintenance contractor. (They also like to be able to converse in English with laborers on site.)
If you join your state turf assn, and go to conferences, you will get a good exposure to the whole turf industry. Also joining a state nursery (or nursery & landscape) assn, and going to their conferences and seminars, will give you insight into the ornamental field. You may even look into these type of groups in adjacent states. At our IN conferences, we often have speakers from IL, OH, & KY. By working at the state level, you will be getting information and meeting people who are in the same geographic area dealing with the same problems and ideas.